Derivation of Heat Conductivity from Temperature and Heat Flux Measurements in Soil

The general inverse problem formulation for a heat conductance equation is adopted for the types of measurement routinely carried out in the soil active layer. The problem solution delivers a constant thermal diffusivity coefficient a0 (in general, different from true value a) and respective heat conductivity λ0 for the layer, located between two temperature sensors and equipped with a temperature or heat flux sensor in the middle. We estimated the error of solution corresponding to systematic shifts in sensor readings and mislocation of sensors in the soil column. This estimation was carried out by a series of numerical experiments using boundary conditions from observations on Mukhrino wetland (Western Siberia, Russia), performed in summer, 2019. Numerical results were corroborated by analytical estimates of inverse problem solution sensitivity derived from classical Fourier law. The main finding states that heat conductivity error due to systematic shifts in temperature measurements become negligible when using long temperature series, whereas the relative error of a is approximately twice the relative error of sensor depth. The error a0−a induced by heat flux plate displacement from expected depth is 3–5 times less than the same displacement of thermometers, which makes the requirements for heat flux installation less rigid. However, the relative errors of heat flux observation typical for modern sensors (±15%) cause the uncertainty of a above 15% in absolute value. Comparison of the inverse problem solution to a estimated from in situ moss sampling on Mukhrino wetland proves the feasibility of the method and corroborates the conclusions of the error sensitivity study.